Export object to a 3ds file error
The solution ...

I found out that your model have a total of 112,330 triangles.
and on the wiki it states that 3ds have these shortcomings:


All meshes must be made of triangles.
All texture filenames are limited to the 8.3 DOS format.
The number of vertices and polygons per mesh is limited to 65536.
Accurate vertex normals cannot be stored in the .3ds file. Instead "smoothing groups" are used so that the receiving program can recreate a  representation of the vertex normals.
Object, light and camera names are limited to 10 characters. Material names are limited to 16 characters.
Directional light sources are not supported.


WHY?
So why was it having problem exporting even though you have the faces count
at 24,000 and vertices at 56,000 range? Both numbers comply with the 3ds format's limitation. The problem is that all the faces needs to be triangles
, the export operation convert all non triangle surface to triangles before saving. Moreover, you can test this. If you do CTRL + T and triangulate your mesh in edit mode you will realise that your mesh exceed that limitation.

After triangulation it sits at 112,330 faces! Which is equal to the number of triangles. In the case of 3ds format, the triangles count is the number we want to keep an eye on.

HOW?
Notice the word per mesh ... that is our key to exporting high poly mesh.
What I did was break up your mesh into 3 portion and then export them in
one single 3ds file.

DOWNLOAD THE BLEND FILE HERE

Try exporting the file and reimporting into blender should give no more problems
now.

A Little History of Polygon
A long time ago in the early days of CGI, polygon refers to triangles.
It's not until much later, more artist prefers to work with 4 sided polygons
then 3 sided ones. (Less clutter on screen, better work flow!) Sometimes when we read about some legacy format that were created in the 1980s, polygon may very well meant triangles!